OK, folks. I got the solution. As advised, I visited the Planet Bike website and looked at tail lights. I saw no mounting brackets, but I did see a light that I liked a lot. It was called Grateful Red and it came in two flavors: battery operated and re-chargable via a USB port (which contains a lithium-ion polymer battery like the kind found in digital cameras and cell phones). I opted for the latter because I liked the re-chargablility and the fact that the the mini-USB port (actually a mini-HDMI connector if you want to be technical). The kit came with a T-shaped mounting bracket that has four holes with recessed hex-head fixtures for the mounting bolts. As one poster pointed out, a single mounting hole will allow the light to twirl. But since the bracket has the recessed hex heads and the kit comes with the nuts, bolts, flat washers, and locking washers I was able to snug it up nice and tight and that doesn't seem to be a problem.
It worked perfectly on my very low clearance (due to the short length of the "Mark's" mini-rack) between the rack mounting hole and the fender. I did have to cut off a securing tab on the light's mounting bracket to get it to fit into that tight space, but didn't consider it big deal because the light slides on to the bracket very snuggly and the fact that it's a vertical application. The light works in three modes: steady, strobe-like flashing, and one flash-per-second. I prefer the last of these because sends approaching vehicle, bikes, or whatever, that you're there without annoying excessive flashing. If you want more details on the light and its mounting and charging accessories surf into the Planet Bike website. Meanwhile, here are some pic's on how it looks: